| HPS 0628 | Paradox | |
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1. In a lottery, players can choose a number and, if that number is drawn, they win the prize. An astute player decides to choose numbers with the following strategy. The player will run his own lottery privately using the same range of possible numbers. If his lottery delivers some number--say 1,234--he will then not choose that number in the real lottery. He reasons that the chance of both lotteries coming up with the same number is very small. There is a much greater chance that the two lotteries have different numbers.
Does this strategy give the player an advantage? Explain.
2. Four fair coins are tossed.
2a. What is the outcome space?
2b. What is the expectation for the number of heads?
2c. What is the most likely number of number of heads?
2d. Consider the relative numbers of heads and tails. Which is more likely: that we have the same number of each? Or that we have three times as many of one as of the other?
2e. How are the answers to 2b. and 2c. compatible with the answer to 2d.?